Related papers: Typhoon eye trajectory based on a mathematical mod…

We present numerical simulations of steady, laminar, axisymmetric convection of a Boussinesq fluid in a shallow, rotating, cylindrical domain. The flow is driven by an imposed vertical heat flux and shaped by the background rotation of the…

We consider the dynamics of two-phase fluids, in particular the moving contact line, on a solid substrate. The dynamics are governed by the sharp-interface model consisting of the incompressible Navier-Stokes\slash Stokes equations with the…

In a two-dimensional model of the planetary atmosphere the compressible convective flow of vorticity represents a strong nonlinearity able to drive the fluid toward a quasi-coherent vortical pattern. This is similar to the highly organised…

Consider the anisotropic Navier-Stokes equations as well as the primitive equations. It is shown that the horizontal velocity of the solution to the anisotropic Navier-Stokes equations in a cylindrical domain of height $\varepsilon $ with…

We investigate the long time behavior of solutions to a shape and topology optimization problem with respect to the time-dependent Navier--Stokes equations. The sought topology is represented by a stationary phase-field that represents a…

Accurate prediction of typhoon trajectories is essential for mitigating the impact of these extreme weather events. This study proposes a functional data analysis (FDA) framework for modeling and forecasting typhoon paths using historical…

In the face of escalating climate changes, typhoon intensities and their ensuing damage have surged. Accurate trajectory prediction is crucial for effective damage control. Traditional physics-based models, while comprehensive, are…

Tropical cyclones are among the most consequential weather hazards, yet estimates of their risk are limited by the relatively short historical record. To extend these records, researchers often generate large ensembles of synthetic storms…

Some implications of the simplest accounting of defects of compatibility in the velocity field on the structure of the classical Navier-Stokes equations are explored, leading to connections between classical elasticity, the elastic theory…

This report presents a low computational and cognitive complexity, stable, time accurate and adaptive method for the Navier-Stokes equations. The improved method requires a minimally intrusive modification to an existing program based on…

We consider a time discretization of incompressible Navier-Stokes equations with spatial periodic boundary conditions in the vorticity-velocity formulation. The approximation is based on freezing the velocity on time subintervals resulting…

Exponential stabilization to time-dependent trajectories for the incompressible Navier-Stokes equations is achieved with explicit feedback controls. The fluid is contained in two-dimensional spatial domains and the control force is, at each…

In this work, we present a parametric finite element approximation of two-phase Navier-Stokes flow with viscoelasticity. The free boundary problem is given by the viscoelastic Navier-Stokes equations in the two fluid phases, connected by…

Extratropical cyclones are large-scale weather systems which are often the source of extreme weather events in Northern Europe, often leading to mass infrastructural damage and casualties. Such systems create a local vorticity maxima which…

Time-periodic solutions to the Navier-Stokes equations that govern the flow of a viscous liquid past a three-dimensional body moving with a time-periodic velocity are investigated. The net motion of the body over a full time-period is…

We develop, analyze, and test an approximate, global data assimilation/synchronization algorithm based on purely local observations for the two-dimensional Navier-Stokes equations on the torus. We prove that, for any error threshold, if the…

We consider an evolution system modeling a flow of colloidal particles which are suspended in an incompressible fluid and accounts for colloidal crystallization. The system consists of the Navier-Stokes equations for the volume averaged…

This note studies the mechanism of turbulent energy cascade through an opportune bifurcations analysis of the Navier--Stokes equations, and furnishes explanations on the more significant characteristics of the turbulence. A statistical…

The large scale atmospheric vortices (tropical cyclones, tornadoes) are complex physical systems combining thermodynamics and fluid-mechanical processes. The well known tendency of vorticity to self-organization, an universal property of…

Tracks of typhoons are predicted using satellite images as input for a Generative Adversarial Network (GAN). The satellite images have time gaps of 6 hours and are marked with a red square at the location of the typhoon center. The GAN uses…